Stir in water, beans, and broth; heat to boiling on medium-high. Reduce heat to low and simmer, uncovered, 15 minutes to blend flavors.

Ladle 3 cups soup into blender; cover, with center part of cover removed to allow steam to escape, and blend until pureed. Stir puree into soup in saucepot; heat through on medium. Stir in cilantro and lime juice, and garnish with cilantro sprigs to serve. Makes about 6 1/2 cups.